SECTION VI.

DEFINITIONS.

1. A right or direct sphere is that which has the poles in the horizon, and the equator and all the parallels of latitude perpendicular to it.

2. An oblique sphere is that which has one of the poles elevated above the horizon less than 90 degrees, and the other depressed below it; the equator and parallels of latitude form, with the horizon, oblique angles.

3. A parallel sphere is that which has the equator in the horizon, and the poles in the zenith and nadir.

4. Twilight is that medium between light and darkness which happens in the morning before sun-rise, and in the evening after sun-set.

5. The crepusculum is a small circle parallel to the horizon, and 18° below it, where the twilight begins and ends.

In Adams's globes it is marked out by a wire circle, fixed 18° below the horizon.

OF TWILIGHT.

As soon as the sun comes within 18° of the horizon, its rays strike the higher parts of the atmosphere, and, being refracted and reflected to every part, occasion that agree ably gradual transition from darkness to light, called twilight.

In the same manner in the evening, after the sun sets, its rays strike upon the higher parts of the atmosphere, until it is more than 18° below the horizon: this prevents us from being suddenly deprived of the light of the sun.

The benefits of twilight are obvious. A change so great, as from the darkness of midnight to the splendour of noon-day, would probably be injurious to the sight; and it would be unpleasant to all, and in many cases very dangerous to travellers, to be involved in darkness without timely notice of its approach.

In all countries situated near the equator, twilight is of much shorter duration than it is in countries of high latitudes; for at the equator the sun rises and sets perpendicularly, but to places at a great distance from the equator it rises and sets very obliquely; and hence it requires a longer time to go 18° below the horizon.

At the latitude of 49° N. twilight continues the whole night on June 21st; and, at places still farther north, it continues the whole night, for a certain number of days before and after the summer solstice. At London there is no total darkness from May 28th till July 20th.

Twilight continues, at the north pole, from September 22d, when the sun sets, to November 12th,-a space of 51 days. Twilight first appears again there about the 30th of January, and continues till sun-rise on March 21st. Thus, though the inhabitants (if any) at the north pole never see the sun for 6 months, yet, out of that time, they have twilight for 14 weeks. The time that they receive no light from the sun is only 12 weeks; and, during that time, the moon is 6 weeks above the horizon.

In this section it is attempted to show, by the globe, the cause of day and night, and also the cause of the variety of the seasons, by elevating the globe, first for the equinoxes, then for the summer and winter solstices. The next problem shows where the sun is rising and setting, and where it is noon and midnight at any time. Then

follow two problems on the twilight; the first to find at what places it is twilight at any given time,-the next to find the duration of twilight on any given day, at any given place. By the last problem it may be seen at what places an eclipse of the moon will be visible.

PROBLEM XXXI.

To shew, by the globe, the cause of day and night.

The sun, shining upon the earth, illuminates only that half of it which is turned towards him; whilst the other half, being turned from him, is in darkness.

But, as the earth turns round on its axis, from west to east, once in 24 hours, every meridian upon the earth will, in that time, successively enjoy the light of the sun, and be deprived of it.

Having elevated the globe for the sun's declination, so that the sun may be in the zenith, the horizon will be the terminator, or boundary circle, of light and darkness; that half of the earth which is above the horizon being in the light, and that half which is below the horizon being in darkness.

Suppose, now, a patch to be put upon a globe to represent any place, and the globe to be turned round from west to east; when the place comes to the western side of the horizon, the sun appears to the inhabitants of that place to be rising in the east; but it is more properly the inhabitants of that place rising in the west. Continue to turn the globe round, and the place will ascend higher towards the meridian, which causes the sun to appear to ascend towards the meridian in a contrary direction.

When the place has arrived at the meridian, it will then

be noon there, and the sun will be at his greatest altitude for that day.

As you continue to turn the globe, the place will gradually recede from the meridian, and descend towards the eastern horizon, which will cause the appearance of the sun descending towards the west. When the place has arrived at the eastern horizon, as it is then going below the terminator, or boundary of light and darkness, the sun will appear to be setting in the west.

The place having gone below the horizon, and being now at a greater distance than 90° from that point where the sun is vertical, is deprived of his light, and continues in darknesɛ till, by the revolution of the earth, it arrives again at the western horizon,-when the sun will appear to rise as before.

It is evident that the sun will be rising at the same instant of time to all places that are on the western side of the horizon, and that it will be setting at the same time to all places that are on the eastern side of the horizon.

PROBLEM XXXII.

To shew, by the globe, the cause of the variety of the

seasons.

It may be seen, at any time, in what manner the globe is cut by the circle of light and darkness, by making the horizon to represent it. The sun's rays extending to the distance of 90° from the point to which he is vertical, when the sun is in the equinoctial, the boundary circle will pass through the poles, each being 90° distant from the equator; hence, when the sun is in the equator, that the horizon may be made to represent the terminator, or boundary

circle of light and darkness, the poles must be made to coincide with it.

When the sun is in the tropic of cancer, being 231° farther to the north than before, his rays will extend 2310 beyond the north pole on the opposite meridian? but they will not reach the south pole by 2310, that is, they will extend only to the antarctic circle, being 90° distant from tropic of cancer: hence, to make the horizon the terminator in this case, the north pole must be elevated 23° above the horizon.

When the sun is in the tropic of capricorn, the reverse of this will take place; that is, the sun's rays will extend 231 beyond the south pole on the opposite meridian, but will extend only as far north as the arctic circle: hence, to make the horizon the terminator in this case, the south pole must be elevated 2310 above the horizon.

We shall now proceed to place the globe in these three several positions.

1.-To place the globe in the same situation as the earth is at the time of the equinoxes.

Having brought both poles to coincide with the horizon, the equator and all the parallels of latitude will make right angles with the horizon; and the globe, in this position, is called a right sphere.

The equator, as well as the parallels of latitude, are cut into two equal parts by the horizon; hence the days and nights are then equal at all places.

This will be exemplified by taking three places that have the same longitude, but different latitudes :-Suppose London, a place upon the equator having the same meridian with London, and the antoeci of London. Put a patch